Sequential Importance Resampling (SIR) is a method of particle filtering that can be used for sequential data assimilation [1]}, [2]}. In SIR, the posterior is approximated by the analysis of an ensemble of simulations, or "particles". The prior is approximated by generating an ensemble of simulations that reflects the uncertainty in the models initial and boundary conditions. The model evolves the ensemble forward in time, until a set of observations are available. At the observation time, an analysis is performed which weights each simulation in accordance with its agreement with the observations. Then, this weighted ensemble is used to generate a new ensemble of simulations which are closer to the observations. The model then resumes advancing the simulations forward in time, until the next set of observations are available. The data assimilation proceeds in this way, performing sequential analysis steps when observations are available. The posterior distribution, at some specific time, is approximated by the distribution of the ensemble after an analysis step.
